You cannot claim that 'care is care' - as if there's an equivalence, and then also claim that 'No two people have exactly the same needs' as if there's a difference. Literally, what you seem to be saying is 'everyone needs care'. Yes, that's true. But we're specifically talking about Carers Allowance for disabled people here.
Having a baby is a choice, you can choose not to, that's why abortion exists.
Elderly care happens within a specific timeframe, i.e. the person has to be elderly. There's a difference between caring for someone for 10 years and caring for someone for 60 years.
I don't care about your direct first hand experience, it's just an anecdote, it's evidence of nothing. I care about data and facts.
I'm shocked that you don't seem to understand there's a link between having a government that gives its mates backhanders, that same government allowing corporate tax evasion on a massive scale, and newspapers friendly to the government and corporations peddling stories about scarcity. It's not about 'infinite' resources, it's about using the finite resources we have morally and responsibly.
Finally, I could be wrong, but I think I see where you're coming from with regard to the 'enormous care bill' because you're right. Give it 10 or 20 years and, I believe, we're going to see the biggest shift of wealth from the private individual to the corporate sector ever. All that property wealth that people think they've got, that they imagine is going to be inherited, nah, I it's going to end up paying astronomical care bills. To avoid this, we need an argument that suggests it's right and proper to care for the elderly, badly and informally, to stop them having to go into homes for professional help. It's an effort to normalise casual brutality to preserve the inheritance.